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Opportunistic Spatial Orthogonalization (OSO) is a cognitive radio scheme that allows the existence of secondary users and hence increases the sum throughput, even if the primary user occupies all the frequency bands all the time. The key idea is to exploit the spatial dimensions to orthogonalize users and hence minimize interference. However, unlike the time and frequency dimensions, there is no universal basis for the set of all multi-dimensional spatial channels, which motivated the development of OSO. On one hand, OSO can be viewed as a multi-user diversity scheme that exploits the channel randomness and independence. On the other hand, OSO can be interpreted as an opportunistic interference alignment scheme for asymmetric users, where the interference from multiple secondary users is opportunistically aligned at the direction that is orthogonal to the primary user's signal space. In the case of multiple-input multiple-output (MIMO) channels, the OSO scheme can be interpreted as “riding the peaks” over the eigen-channels, and ill-conditioned MIMO channel, which is traditionally viewed as detrimental, is shown to be beneficial with respect to the sum throughput. Throughput advantages are thoroughly studied, both analytically and numerically.